1. Field of the Invention
The present invention relates to computerized methods and systems for modeling thermal systems, and particularly to a method of modeling thermal problems using a non-dimensional finite element method that relies on the variational principle.
2. Description of the Related Art
The application of non-dimensional analysis is very common for heat transfer problems, where most of the experimental correlations are given as a function of non-dimensional groups. However, in order to generate numerical solutions for the differential and integral equations of thermal systems, which may not have analytical solutions, the solution of heat transfer problems is commonly based on finite element or finite volume, using quantities with dimensions.
Conventionally, a commercial finite element method-based system, such as ANSYS (which is basically a dimensional code), is used for the solution of dimensional problems, and then the finite element results are converted into non-dimensional form. Rather than performing this two-step process, which may be very heavy on computational power and time, it would be desirable to obtain the finite element formulation in a non-dimensional form such that the finite element results may be directly produced without dimensions.
Further, conventional finite element techniques are only valid for a specific problem. It would be desirable to provide a general non-dimensional finite element method that is valid for an entire class of problems.
Thus, a method of modeling thermal problems using a non-dimensional finite element method solving the aforementioned problems is desired.